99-278 Simon B.
A Feynman-Kac Formula for Unbounded Semigroups (12K, LaTeX) Jul 26, 99
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Abstract. We prove a Feynman-Kac formula for Schr\"odinger operators with potentials $V(x)$ that obey (for all $\varepsilon >0$) \[ V(x) \geq -\varepsilon |x|^2 - C_\varepsilon. \] Even though $e^{-tH}$ is an unbounded operator, any $\varphi, \psi \in L^2$ with compact support lie in $D(e^{-tH})$ and $\langle \varphi, e^{-tH}\psi\rangle$ is given by a Feynman-Kac formula.

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